This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

Testing Linearity in Cointegrating Relations with an Application to Purchasing Power Parity

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Seung Hyun Hong (Dept. of Economics, Concordia University)
Peter C. B. Phillips () (Cowles Foundation, Yale University; University of Auckland & University of York)

Additional information is available for the following registered author(s):

Abstract

This paper develops a linearity test that can be applied to cointegrating relations. We consider the widely used RESET specification test and show that when this test is applied to nonstationary time series its asymptotic distribution involves a mixture of noncentral chi^2 distributions, which leads to severe size distortions in conventional testing based on the central chi^2. Nonstationarity is shown to introduce two bias terms in the limit distribution, which are the source of the size distortion in testing. Appropriate corrections for this asymptotic bias leads to a modified version of the RESET test which has a central chi^2 limit distribution under linearity. The modified test has power not only against nonlinear cointegration but also against the absence of cointegration. Simulation results reveal that the modified test has good size infinite samples and reasonable power against many nonlinear models as well as models with no cointegration, confirming the analytic results. In an empirical illustration, the linear purchasing power parity (PPP) specification is tested using US, Japan, and Canada monthly data after Bretton Woods. While commonly used ADF and PP cointegration tests give mixed results on the presence of linear cointegration in the series, the modified test rejects the null of linear PPP cointegration.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://cowles.econ.yale.edu/P/cd/d15a/d1541.pdf
File Format: application/pdf
File Function:
Download Restriction: no

Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1541.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 44 pages
Date of creation: Dec 2005
Date of revision:
Handle: RePEc:cwl:cwldpp:1541

Contact details of provider:
Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
More information through EDIRC

Order Information:
Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

For technical questions regarding this item, or to correct its listing, contact: (Glena Ames).

Related research
Keywords: Nonlinear cointegration; Specification test; RESET test; Noncentral chi^2 distribution;

Other versions of this item:

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Ermini, Luigi & Granger, Clive W. J., 1993. "Some generalizations on the algebra of I(1) processes," Journal of Econometrics, Elsevier, vol. 58(3), pages 369-384, August. [Downloadable!] (restricted)
    Other versions:
  2. O'Connell, Paul G. J., 1998. "The overvaluation of purchasing power parity," Journal of International Economics, Elsevier, vol. 44(1), pages 1-19, February. [Downloadable!] (restricted)
  3. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation, Yale University. [Downloadable!]
  4. Yoosoon Chang & Joon Y. Park & Peter C.B. Phillips, 1999. "Nonlinear Econometric Models with Cointegrated and Deterministically Trending Regressors," Cowles Foundation Discussion Papers 1245, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  5. Porter, Richard D. & Kashyap, Anil K., 1984. "Autocorrelation and the sensitivity of reset," Economics Letters, Elsevier, vol. 14(2-3), pages 229-233. [Downloadable!] (restricted)
  6. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation, Yale University. [Downloadable!]
  7. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-61, January.
    Other versions:
  8. Zhijie Xiao & Peter C.B. Phillips, 2001. "A CUSUM Test for Cointegration Using Regression Residuals," Cowles Foundation Discussion Papers 1329, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  9. repec:cup:macdyn:v:5:y:2001:i:4:p:533-76 is not listed on IDEAS
  10. Peter C.B. Phillips, 1998. "Econometric Analysis of Fisher's Equation," Cowles Foundation Discussion Papers 1180, Cowles Foundation, Yale University. [Downloadable!]
  11. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
    Other versions:
  12. Moshiri, Saeed & Cameron, Norman E & Scuse, David, 1999. "Static, Dynamic, and Hybrid Neural Networks in Forecasting Inflation," Computational Economics, Springer, vol. 14(3), pages 219-35, December. [Downloadable!]
  13. Michael, Panos & Nobay, A Robert & Peel, David A, 1997. "Transactions Costs and Nonlinear Adjustment in Real Exchange Rates: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 105(4), pages 862-79, August.
  14. Linda F. DeBenedictis, & David E. A. Giles, 1998. "Robust Specification Testing in Regression: The FRESET Test and Autocorrelated Disturbances," Econometrics Working Papers 9806, Department of Economics, University of Victoria. [Downloadable!]
  15. Kenneth A. Froot & Kenneth Rogoff, 1996. "Perspectives on PPP and Long-Run Real Exchange Rates," NBER Working Papers 4952, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  16. Thursby, Jerry G, 1981. "A Test Strategy for Discriminating between Autocorrelation and Misspecification in Regression Analysis," The Review of Economics and Statistics, MIT Press, vol. 63(1), pages 117-23, February. [Downloadable!] (restricted)
  17. Lee, Tae-Hwy & White, Halbert & Granger, Clive W. J., 1993. "Testing for neglected nonlinearity in time series models : A comparison of neural network methods and alternative tests," Journal of Econometrics, Elsevier, vol. 56(3), pages 269-290, April. [Downloadable!] (restricted)
  18. Kenneth Rogoff, 1996. "The Purchasing Power Parity Puzzle," Journal of Economic Literature, American Economic Association, vol. 34(2), pages 647-668, June. [Downloadable!] (restricted)
  19. Serena Ng & Pierre Perron, 2001. "PPP May not Hold After all: A Further Investigation," Economics Working Paper Archive 466, The Johns Hopkins University,Department of Economics. [Downloadable!]
  20. Rudiger Dornbusch, 1985. "Purchasing Power Parity," NBER Working Papers 1591, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  21. Breitung, Jorg, 2001. "Rank Tests for Nonlinear Cointegration," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 331-40, July.
  22. Alan M. Taylor, 2002. "A Century Of Purchasing-Power Parity," The Review of Economics and Statistics, MIT Press, vol. 84(1), pages 139-150, February. [Downloadable!] (restricted)
    Other versions:
  23. Rustam Ibragimov & Peter C.B. Phillips, 2004. "Regression Asymptotics Using Martingale Convergence Methods," Cowles Foundation Discussion Papers 1473, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  24. Siu Fai Leung & Shihti Yu, 2001. "The sensitivity of the RESET tests to disturbance autocorrelation in regression analysis," Empirical Economics, Springer, vol. 26(4), pages 721-726. [Downloadable!] (restricted)
  25. Baghestani, Hamd, 1991. "Application of the RESET test to the original Andersen-Jordan equation," Journal of Macroeconomics, Elsevier, vol. 13(1), pages 157-169. [Downloadable!] (restricted)
  26. P.H. Franses & D.J. van Dijk, 2002. "A simple test for PPP among traded goods," Econometric Institute Report 255, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
    Other versions:
  27. Peter C. B. Phillips, 2001. "Descriptive econometrics for non-stationary time series with empirical illustrations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 389-413. [Downloadable!]
    Other versions:
  28. Lo, Ming Chien & Zivot, Eric, 2001. "Threshold Cointegration And Nonlinear Adjustment To The Law Of One Price," Macroeconomic Dynamics, Cambridge University Press, vol. 5(04), pages 533-576, September. [Downloadable!]
    Other versions:
  29. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June. [Downloadable!]
    Other versions:
  30. Vitaliano, Donald F., 1987. "On the estimation of hospital cost functions," Journal of Health Economics, Elsevier, vol. 6(4), pages 305-318, December. [Downloadable!] (restricted)
  31. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Blackwell Publishing, vol. 57(1), pages 99-125, January. [Downloadable!] (restricted)
  32. Dumas, Bernard, 1992. "Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 5(2), pages 153-80. [Downloadable!] (restricted)
  33. Phillips, Peter C B, 1995. "Fully Modified Least Squares and Vector Autoregression," Econometrica, Econometric Society, vol. 63(5), pages 1023-78, September. [Downloadable!] (restricted)
    Other versions:
  34. Franses, Ph.H.B.F. & Dijk, D.J.C. van, 2002. "A simple test for PPP among traded goods," Econometric Institute Report EI 2002-02 Revision_Date:, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
  35. Froot, Kenneth A. & Rogoff, Kenneth, 1995. "Perspectives on PPP and long-run real exchange rates," Handbook of International Economics, in: G. M. Grossman & K. Rogoff (ed.), Handbook of International Economics, edition 1, volume 3, chapter 32, pages 1647-1688 Elsevier. [Downloadable!] (restricted)
  36. Peters, Simon, 2000. "On the Use of the RESET Test in Micro-econometric Models," Applied Economics Letters, Taylor and Francis Journals, vol. 7(6), pages 361-65, June. [Downloadable!] (restricted)
  37. Granger, Clive W J, 1995. "Modelling Nonlinear Relationships between Extended-Memory Variables," Econometrica, Econometric Society, vol. 63(2), pages 265-79, March. [Downloadable!] (restricted)
  38. repec:bep:sndecm:7:2003:2:1099-1099 is not listed on IDEAS
  39. Jeffrey A. Frankel & Andrew K. Rose, 1994. "A Survey of Empirical Research on Nominal Exchange Rates," NBER Working Papers 4865, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  40. Saikkonen, Pentti & Choi, In, 2004. "Cointegrating Smooth Transition Regressions," Econometric Theory, Cambridge University Press, vol. 20(02), pages 301-340, April. [Downloadable!]
  41. Peter Pedroni, 2001. "Purchasing Power Parity Tests In Cointegrated Panels," The Review of Economics and Statistics, MIT Press, vol. 83(4), pages 727-731, November. [Downloadable!] (restricted)
  42. Joon Y. Park & Peter C. B. Phillips, 2000. "Nonstationary Binary Choice," Econometrica, Econometric Society, vol. 68(5), pages 1249-1280, September.
    Other versions:
  43. Mussa, Michael, 1976. " The Exchange Rate, the Balance of Payments and Monetary and Fiscal Policy under a Regime of Controlled Floating," Scandinavian Journal of Economics, Blackwell Publishing, vol. 78(2), pages 229-48.
  44. Phillips, Peter C B, 1983. "ERAs: A New Approach to Small Sample Theory," Econometrica, Econometric Society, vol. 51(5), pages 1505-25, September. [Downloadable!] (restricted)
    Other versions:
  45. Lothian, James R & Taylor, Mark P, 1996. "Real Exchange Rate Behavior: The Recent Float from the Perspective of the Past Two Centuries," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 488-509, June. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Qiying Wang & Peter C.B. Phillips, 2006. "Asymptotic Theory for Local Time Density Estimation and Nonparametric Cointegrating Regression," Cowles Foundation Discussion Papers 1594, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  2. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2006. "Purchasing Power Parity: The Irish Experience Re-visited," Trinity Economics Papers tep200615, Trinity College Dublin, Department of Economics. [Downloadable!]
Statistics
Access and download statistics

Did you know? You too can volunteer for RePEc, for example by encouraging others to use our services.

This page was last updated on 2009-11-9.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.